Conducted a survey (pre and post) on four questions using Likert scale. Based on the number of responses for agree and strongly agree pre and post intervention, computed the relative improvement. I want to know if this relative improvement is statistically significant or not. What test should I do?
A simple test for changes in paired samples is the Wilcoxon signed-rank test. It's nonparametric, so Likert data won't be a problem. You can use this on each item if you like (and correct for familywise error inflation if appropriate), or if your items are all supposed to measure the same construct, you can adopt classical test theory assumptions and sum or average them...or you could estimate factor scores using a rating scale model. This is an item response theory approach that produces index scores as continuous data, which might then permit a paired-samples t-test as well. However, there's no guarantee that these factor scores would be normally distributed, and the whole process may take a fair amount of data. There are also bootstrap and Bayesian methods for these analyses, though I'm less familiar with them.